An unpublished theorem of Solovay on OD partitions of reals into two non-OD parts, revisited

Author:

Enayat Ali1,Kanovei Vladimir2

Affiliation:

1. Department of Philosophy, Linguistics, and Theory of Science, University of Gothenburg, Box 200, 40530 Gothenburg, Sweden

2. Institute for Information Transmission Problems of the Russian Academy of Sciences (Kharkevich Institute), 19, Build.1, Bolshoy Karetny per., Moscow 127051, Russia

Abstract

A definable pair of disjoint non-OD sets of reals (hence, indiscernible sets) exists in the Sacks and 𝔼0-large generic extensions of the constructible universe L. More specifically, if [Formula: see text] is either Sacks generic or 𝔼0-large generic real over L, then it is true in L[a] that there is a lightface [Formula: see text] equivalence relation [Formula: see text] on the [Formula: see text] set [Formula: see text] with exactly two equivalence classes, and both those classes are non-OD sets.

Funder

RFBR

Publisher

World Scientific Pub Co Pte Ltd

Subject

Logic

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